Comparative Analysis of Mcnemar's Test and Liddell's Exact Test for Assessing Marginal Homogeneity

In this study, we aim to identify the preferred test for assessing marginal homogeneity, compare McNemar’s and Liddell's exact tests, and determine the conditions under which each test is most appropriate. A Monte Carlo simulation approach was employed to develop and analyze both tests. The power and Type I error rates were computed for various sample sizes, effect sizes, and significance levels (α). Random samples ranging from 20 to 1000 were analyzed over 500 iterations. Three different hypothetical scenarios were used to evaluate the performance of McNemar’s test and Liddell's exact test, considering different P12 and P21 values and using significance levels of 1% and 10%. The results indicate that Liddell's exact test is generally preferable, mainly when the effect sizes are moderate to large across nearly all sample sizes. McNemar’s test is not recommended for sample sizes of 20 or fewer. Liddell’s exact test is more advantageous when the proportions are small and close together, especially with larger sample sizes.